The objective of this study is to determine whether a short course of intensive therapy during early remission of childhood acute lymphocytic leukemia (ALL) will result in prolonged remission duration and/or increase eventual disease-free survival. Intensification will utilize agents (adriamycin, cyclophosphamide) which are not part of prior or subsequent chemotherapy. Patients receiving intensification will be monitored for increased toxicity as well as for changes in disease control.